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Full-Text Articles in Science and Technology Studies
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Associate Professor Adam Rennie
We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state.
Families Of Type Iii Kms States On A Class Of C-Algebras Containing On And Qn, A L. Carey, J Phillips, I F. Putnam, A Rennie
Families Of Type Iii Kms States On A Class Of C-Algebras Containing On And Qn, A L. Carey, J Phillips, I F. Putnam, A Rennie
Associate Professor Adam Rennie
We construct a family of purely infinite C¤-algebras, Q¸ for ¸ 2 (0, 1) that are classified by their K-groups. There is an action of the circle T with a unique KMS state à on each Q¸. For ¸ = 1/n, Q1/n »= On, with its usual T action and KMS state. For ¸ = p/q, rational in lowest terms, Q¸ »= On (n = q − p + 1) with UHF fixed point algebra of type (pq)1. For any n > 1, Q¸ »= On for infinitely many ¸ with distinct KMS states and UHF fixed-point algebras. For any ¸ …